• Ellouze, Imen
  • Received : 2013.01.05
  • Published : 2014.01.01


In this paper, we deal with the problem of practical observer design and the practical stabilization for a class of perturbed impulsive systems. We show that, under the classical conditions of uniform complete controllability and uniform complete observability of the nominal system without impulsive effects, it is possible to design an observer controller for a class of perturbed linear impulsive system when the origin is not an equilibrium point.


impulsive perturbed systems;practical observer design;practical stabilization;separation principle


  1. B. Benhamed, I. Ellouze and M. A. Hammami, Practical uniform stability of nonlinear differential delay equations, Mediterr. J. Math. 8 (2011), no. 4, 603-616.
  2. I. Ellouze and M. A. Hammami, On the practical stability of impulsive control systems with multiple time delays, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 20 (2013), 341-356.
  3. A. M. Enrique and A. L. Douglas, State estimation for linear impulsive systems, In Proc. Amer. Control Conf. (2009), 1183-1188.
  4. J.-P. Gauthier and I. Kupka, Deterministic Observation Theory and Applications, Cambridge Math. Lib., 2000.
  5. E. Kruger-Thiemer, Formal theory of drug dosage regiments, I. J. Theoret. Biol. 13 (1966), 212-235.
  6. V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
  7. X. Liu, Stability of impulsive control systems with time delay, Math. Comput. Modelling 39 (2004), no. 4-5, 511-519.
  8. P. Naghshtabrizi, I. P. Hespanha and A. R. Teel, Exponential stability of impulsive systems with application to uncertain sampled-data systems, Systems Control Lett. 57 (2008), no. 5, 378-385.
  9. F. L. Pereira and G. N. Silva, Stability for impulsive control systems, Dyn. Syst. 17 (2002), no. 4, 421-434.
  10. S. Ruiqing and C. Lansun, An impulsive predator-prey model with disease in the prey for integrated pest management, Commun. Nonlinear Sci. Numer. Simul. 15 (2009), no. 2, 421-429.
  11. S. Ruiqing, J. Xiaowu and C. Lansun, The effect of impulsive vaccination on an sir epidemic model, Appl. Math. Comput. 212 (2009), no. 2, 305-311.
  12. G. Xie and L. Wang, Controllability and observability of a class of linear impulsive systems, J. Math. Anal. Appl. 304 (2005), no. 1, 336-355.

Cited by

  1. Stability of impulsive systems depending on a parameter vol.39, pp.10, 2016,